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High School Trigonometry: Help and Review31 chapters | 240 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Karin Gonzalez*

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, you will learn the definition of the identity property, discover the four different identity properties and examine examples that clearly illustrate these properties. Following this lesson will be a brief quiz to test your knowledge.

An **identity** is a number that when added, subtracted, multiplied or divided with any number (let's call this number *n*), allows *n* to remain the same. The identity will be either 0 or 1, depending on the operation that we are using. In addition and subtraction, the identity is 0. In multiplication and division, the identity is 1. That means that if 0 is added to or subtracted from *n*, then *n* remains the same. Also, if *n* is multiplied or divided by 1, then *n* remains the same.

The **identity property** states that when you use an operation to combine an identity with a number (*n*), the end result will be *n*:

*n* + Additive Identity (0) = *n*

*n* - Subtractive Identity (0) = *n*

*n* * Multiplicative Identity (1) = *n*

*n*/ Divisive Identity (1) = *n*

How do we know which identity property we're using? That's easy! We can just look at the sign being used in each mathematical expression. The additive identity uses the + sign. The subtractive identity uses the - sign. The multiplicative identity uses the * sign and the divisive identity uses the / sign.

It was mentioned before that the identity is always 0 for addition and subtraction and 1 for multiplication and division. Why is this, you may ask? Let's look deeper at how the operations actually work!

Addition is the process of adding something to something else. So when you add 7 to 0, you're going to get 7. Subtraction is the process of taking away one amount from another amount. So when you subtract 0 from 7, you're going to get 7.

Multiplication is the process of repeated addition. When you multiply a number with another, you are repeatedly adding a number by the number of times stated by the other number. So, if you have 7 * 8, you are repeatedly adding the number 7 eight times. The identity of multiplication is 1, so if you have 7 * 1, you are repeatedly adding 7 one time. That gives us 7.

Division is the process of separating a number into parts. So if we have 7/1, we are separating the number 7 into one part. That would be 7, right? Yes!

If you were to substitute in any other number for 0 or 1 in the above scenarios, the math wouldn't work, which is why the identities are always 0 or 1.

Let's look at some examples for each of the identity properties of addition, subtraction, multiplication and division, starting with the identity property of addition:

Example 1: 100,000,000 + 0 = 100,000,000

Example 2: -67 + 0 = -67

Example 3: (*A* + *B*) + 0 = *A* + *B*

Example 4: You have 6 apples in your fruit basket at home and buy zero apples at the grocery store. You should still have 6 apples in your fruit basket by the time you put away all of your groceries. So, 6 + 0 = 6.

Now let's look at the identity property of subtraction:

Example 1: 432123456765 - 0 = 432123456765

Example 2: -47 - 0 = -47

Example 3: *Y* - 0 = *Y*

Example 4: You have 10 gummy bears that you decide you want to save for later. Therefore, you eat and share zero gummy bears. When you decide to come back and eat the gummy bears, you should still have 10. If you were to translate this word problem into numbers, you would have 10 - 0 = 10.

Now let's look at examples of the identity property of multiplication:

Example 1: 567,000 * 1 = 567,000

Example 2: -567 * 1= -567

Example 3: *X* * 1 = *X*

Example 4: You need two stamps for each envelope you send out because they are heavier than usual. If you only have one envelope, you'll only need two stamps. This can be written with numbers as 2 * 1 = 2.

Finally, let's look at some examples of the identity property of division:

Example 1: 333/1= 333

Example 2: -789/1= -789

Example 3: *X*/1= *X*

Example 4: If you have a 14-piece chocolate bar and divide it by one piece, you get 14 pieces of chocolate. This can be written mathematically as 14/1 = 14.

An **identity** is a number that when added, subtracted, multiplied or divided with any number (let's call this number *n*), allows *n* to remain the same. There are two identities, 0 and 1, in the operations of addition, subtraction, multiplication and division. In addition and subtraction, the identity is 0, and in multiplication and division, the identity is 1.

This lesson should teach you how to:

- Discuss what the identity property is
- Demonstrate how to use the identity property
- Explain why the identities are always 0 and 1

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High School Trigonometry: Help and Review31 chapters | 240 lessons | 1 flashcard set

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